A Study of Accelerated Expansion of the Universe and Time Varying Gravitational Constant in the Framework of Brans-Dicke Theory

A simple mathematical model has been proposed on the basis of generalized Brans-Dicke (BD) theory where, the dimensionless BD parameter is regarded as a function of the scalar field. The gravitational constant is reciprocal of this scalar field. The calculations in this model are based on a very simple ansatz , which has been chosen for the purpose of solving the differential equations most conveniently. This function has been chosen to account for an inter-conversion between the matter and dark energy. This inter-conversion is said to be connected to an interaction that causes the accelerated expansion of the universe. The requirement of a signature flip of the deceleration parameter , which is evident from other studies, sets the boundary conditions to be satisfied by the function , leading to the formulation of its time dependence. A simple empirical relation has been assumed to represent the time dependence of , and the constants in this expression have been determined from the boundary conditions. The parameter has been found to have a negative value. The dependence of upon has been shown graphically. The present model shows that a transition of the universe, from decelerated expansion to accelerated expansion, takes place due to a conversion of matter into dark energy. An increase of gravitational constant with time is found in the present study